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A Pyramidal Evolutionary Algorithm
with Different Inter-Agent Partnering
Strategies for Scheduling Problems
Annual Operational Research Conference 43, Bath, UK, 2001.
This paper combines the idea of a hierarchical distributed genetic algorithm with different inter-agent partnering strategies. Cascading clusters of sub-populations are built from bottom up, with higher-level sub-populations optimising larger parts of the problem. Hence, higher-level sub-populations search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. The effects of different partner selection schemes amongst the agents on solution quality are examined for two multiple-choice optimisation problems. It is shown that partnering strategies that exploit problem-specific knowledge are superior and can counter inappropriate (sub-) fitness measurements.
Dr Uwe Aickelin
School of Computer Science
University of Nottingham
NG8 1BB UK
2
The Nurse Scheduling Problem
Objective:
• To create weekly schedules on ward basis.
• To satisfy working contracts and to have fair schedules.
• To take as many nurses’ requests into
account as possible.
3
Decomposition:
1. Ensuring that nurses present can
cover the overall demand.
2. Scheduling the days and/or nights a
nurse works.
3. Splitting the day shifts into early and
late shifts.
Typical Dimensions of Data:
30 nurses, 3 grade bands, 7 part time
options, 411 different shift patterns,
varying demand levels.
4
The Nurse Model
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pij = penalty cost of nurse i working pattern j
Rks = demand of nurses with grade s on day k
F(i) = set of feasible shift patterns for nurse i
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6
The Mall Model
Shop Income Factors:
• The attractiveness of the area in which the shop is located.
• The total number of shops of the same
type in the mall.
• The size of the shop. • Synergy effects with neighbouring
shops.
7
Constraints:
• Maximum number of shops per shop
type.
• Maximum number of small / medium
/ large shops.
• One shop unit per location.
10
Partnering Strategies
• Rank-Selection (S) based on sub-fitness score
• Random (R)
• Best (B) based on sub-fitness
• Distributed (D) on a toroidal grid
• Joined (J)
• Attractiveness (A): rank-based &
probabilistic depending on created
fitness
• Partner Choice (C): Select Best Partner out of 10.
11
Nurse Scheduling Results
Basic GA:
• Some instances solved satisfactorily
but many infeasible solutions.
Pyramidal GA:
• Marked improvement in performance
but not yet as good as other methods.
Partnering Strategies:
• The more important the sub-fitness
scores, the better they worked: R & D
did poorly, A & C best
12
Mall Problem Results
Basic GA:
• Good results close to theoretic bounds.
Pyramidal GA:
• Far poorer results than with standard GA.
Partnering Strategies:
• All apart from B improve results.
• A & C better than standard GA.
13
Conclusions
• Partnering strategies improve results
(crossover-hillclimber).
• Local search hillclimber still required.
• If sub-fitness measure is good,
selection-based methods work well.
• If sub-fitness measure is poor then
random works as well as others.
• Try Partnering strategies for obtaining sub-fitness scores?